Abstract
Ranking alternatives is a natural way for humans to explain their preferences. It is used in many settings, such as school choice, course allocations and residency matches. Without having any information on the underlying cardinal utilities, arguing about the fairness of allocations requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation whenever it exists. Using simulations, we compare the various fairness criteria in terms of their probability of existence, and their probability of being fair by the underlying cardinal valuations. We find that necessary-DD-proportionality fares well in both measures. We also consider envy-freeness and Pareto optimality under diminishing-differences, as well as chore allocation under the analogous condition - increasing-differences.
Original language | English |
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Pages (from-to) | 471-507 |
Number of pages | 37 |
Journal | Journal of Artificial Intelligence Research |
Volume | 67 |
DOIs | |
State | Published - Mar 2020 |
Bibliographical note
Publisher Copyright:© 2020 AI Access Foundation. All rights reserved.
Funding
Haris Aziz is supported by a Scientia Fellowship. Erel Segal-Halevi was supported by the ISF grant 1083/13, the Doctoral Fellowships of Excellence Program and the Mordecai and Monique Katz Graduate Fellowship Program at Bar-Ilan University. Avinatan Hassidim is supported by ISF grant 1394/16.
Funders | Funder number |
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Mordecai and Monique Katz Graduate Fellowship Program at Bar-Ilan University | 1394/16 |
Israel Science Foundation | 1083/13 |